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Research Laboratories 

of the 
Portland Cement Association 


The Problem of Proportioning Portland 


Cement Raw Mixtures 

— A General View of the Problem 
Part II — Mathematical Study of the Problem 
Part III — Application to Typical Processes 
Part IV — Direct Control of Potential Composition 



JUNE, 1947 


Authorized Reprint from Copyrighted 

Chicago, Illinois 

Jan., Feb., Mar., and Apr. 1947 



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The Problem of Proportioning 

Portland Cement Raw Mixtures 

Part I 

A General View of the Problem 

By L A. DAHL* 

This series of articles on raw 
mixture control will cover 
mathematical studies, ap- 
plication to typical process- 
es, and direct control of po- 
tential composition 

Portland cement clinker is manu- 
factured by heating a finely ground 
mixture of calcareous and argillaceous 
materials in a kiln at a temperature 
of partial fusion. This process is gen- 
erally referred to as "burning." The 
mixture of raw materials is the raw 
mix. There is a considerable variety 
of materials which may be used. For 
example, the calcareous material may 
be limestone, oyster shells or marl. 
The argillaceous material may be 
shale or clay. In some districts cement 
rock is used. This rock contains both 
calcareous and argillaceous constit- 
uents in varying proportions, but in 
approximately the proportions re- 
quired in the raw mix. The principles 
involved in proportioning the raw ma- 
terials are the same for these various 
materials. It will therefore be suffi- 
cient to refer to the materials as lime- 
stone and shale, with the understand- 
ing that the principles and methods 
discussed are applicable to any of 
the raw materials in common use. 

Small changes in proportions of 
limestone and shale have large effect^ 
upon the "burnability" of the raw 
mix; that is, upon the ease with which 
the mix can be burned to a satisfac- 
tory clinker. From the standpoint of 
production, and economy of fuel, ac- 

•Research Chemist. Portland Cement Asso- 
ciation. Chicago. 

curate control of composition is im- 
portant, because periods of easy burn- 
ing do not compensate for loss in 
production and high fuel consumption 
during periods of hard burning. From 
the standpoint of quality of the prod- 
uct, it may be stated that the charac- 
ter of the clinker is influenced both 
by composition and the heat treat- 
ment applied to the mix in the kiln. 
Variations in composition affect burn- 
ability, and therefore affect kiln oper- 
ation. The combination of varying 
composition and the resulting varia- 
tion in kiln operation interferes with 
the attainment of uniformity in the 
product, It is evident from these con- 
siderations that control of composi- 
tion of the raw mix is a critical opera- 
tion, requiring that the proportions of 
limestone and shale, or equivalent ma- 
terials, be accurately controlled. 

Since the early days of the industry 
it has been the practice to subject the 
raw mix to certain rapid chemical 
tests, to determine whether the mix is 
correctly proportioned or to indicate 
needed changes in proportions. With 
such control tests available, it is not 
necessary to proportion the raw ma- 
terials precisely in a single operation. 
For example, in one type of operation 
the limestone and shale may be pro- 
portioned roughly to form preliminary 
raw mixtures, some with too much 
limestone and some with too little. 
These preliminary mixtures are then 
combined in suitable proportions to 
form the final raw mix fed to the 
kilns. Since the preliminary mixtures 
are fairly close to the desired compo- 
sition, the degree of accuracy required 
in the second proportioning operation 
is much less than that which would be 
required if the raw materials were 
proportioned in a single operation. 
This procedure, and other procedures 
designed to eliminate the necessity of 
extremely precise weighing of raw 
materials, would be impossible with- 
out the control tests. 

Function of Raped Control Tests 

Rapid control tests have an impor- 
tant place in all methods of propor- 
tioning raw mixtures. To illustrate 
their function in a simple manner, let 
us assume that a plant has raw mate- 
rials of the compositions indicated in 
the following table, and that they do 
not vary in composition. We will sup- 
pose that the mixture in the last col- 
umn, made with 83,0 per cent lime- 



e A Shale 

No. 1 















SiO 2 3.57 

AI 2 3 1.53 

Fe 2 3 1.64 

CaO 49.71 

MgO 1.20 

Ignition loss 42.35 

Carbonates 91.70 

stone and 17.0 per cent shale, has been 
found to be satisfactory, and that it 

proposed to make this mixture con- 

It would be possible, of course, to 
make the desired mix continuously by 
precise weighing operations. However, 
because of the nature of the raw ma- 
terials and the large quantities to be 
handled, it is difficult to maintain a 
high degree cf precision in the weigh- 
ing equipment. We seek precision, but 
must secure it in some other way. 
Starting without a knowledge of meth- 
ods now in use, we might observe the 
first item in the analyses, the SiO:* 
content. The desired mix contains 
13.71 per cent Si(>2- It can be seen 
from the values for the raw materials 
that the Si0 2 content will be greater 
than 13,71 per cent if more than 17.0 
per cent shale is present and that it 
will be less than 13,71 if less than 17.0 
per cent shale is present. It w T ould 
consequently be possible, even with 
crude weighing equipment, to obtain 
the desired composition by checking 
the Si02 content at various stages of 
the operation, continually working to- 
ward the required SiC>2 content. One 
advantage of selecting SiOo for this 
procedure would be that changes in 
Si0 2 content vtfll clearly indicate cor- 
responding changes in proportions of 
limestone and shale, because of the 
wide difference in S1O2 content of the 

limestone and shale. Referring to the 
analyses, we see that there are other 
constituents which could be chosen for 
the control test instead of Si(>2. The 
CaO content, ignition loss and carbon- 
ate content of the limestone and shale 
are far enough apart to offer possi- 
bilities. A choice is possible, and the 
basis for such a choice is the time 
required for the determination, and 
the simplicity of the method. 

It should be understood from the 
foregoing discussion that the control 
test used in the proportioning opera- 
tion makes it possible to secure accu- 
rate control of proportions with weigh- 
ing equipment which is not capable 
of securing precise proportioning in 
a single operation. In fact, it is pos- 
sible to secure accurate proportions 
by weight without any weighing oper- 
ations in the plant. However, it cannot 
be said that precision in weighing is 
completely eliminated. It is necessary 
to weigh reagents when standardizing 
solutions for control tests, and to 
weigh samples for these tests. What 
we have done in the use of a control 
test is to transfer the precise weigh- 
ing operation, and in some instances 
all of the weighing operations, from 
the plant to the laboratory, where 
conditions are more favorable for pre- 
cision. This is the function of the con- 
trol test. The particular constituent 
determined in the control test is not 
of primary interest. For example, if 
we were to seek to obtain 13.71 'per 
cent Si0 2 in the mix in the operation 
we have been considering, it would 
not be because the Si02 content is of 
special interest, but because when 
this percentage is obtained, all the 
constituents are present in suitable 

method, which 

the amount of 

neutralized by 

raw mix. The 

Control Tests in Common Use 

The control test in most common 
use is the acid-alkali 
is a determination of 
standard acid solution 
a weighed sample of 
number of cubic centimeters of acid 
is multiplied by a factor to obtain the 
equivalent percentage of CaCOj in the 
mix. Since both CaCO ;i and MgCO 
are neutralized by the acid, bt 
MgCO;} neutralizes 1.19 times as )i h 
acid as the same weight of CaCO.*, the 


test value is the sum of the CaC03 
and 1.19 times the MgC0 3 . In this 
study the test value obtained by the 
acid-alkali method will be referred to 
as the carbonate content. 

At some plants the control test is 
a measurement of the volume of CO L > 
gas liberated when a weighed sample 
of raw mix is treated with acid in a 
calcimeter. The volume of gas is con- 
verted to a weight basis, and ex- 
pressed as percentage of CaCOs in the 
sample, by means of tables for taking 
into account both temperature and 
barometric pressure. MgCOa liberates 
CO2, and is included in the same man- 
ner as in the acid-alkali method. The 
test value is similarly referred to as 
the carbonate content. 

In the analyses given in tables in 
this paper the carbonate content is 
obtained by calculation from the for- 

Carbonates = 1.7848 X CaO + 2.4824 X MgO 

The carbonate content obtained by the 
acid-alkali or calcimeter methods may 
not agree with these theoretical val- 
ues, since a small percentage of the 
CaO or MgO may be present in some 
form other than carbonate. In addi- 
tion, some of* the other constituents 
may have a small influence on the 
value obtained by the acid-alkali 
method. However, this does not inter- 
fere at all with the application of 
these methods when the test value to 
be obtained in a correctly proportioned 
mix is known. 

Variations in Raw Material 


The function of control tests has 
been described with reference to an 
ideal condition, in which the raw 
materials do not vary in composition. 
In practice, cement raw materials are 
obtained from natural deposits, and 
these are somewhat variable in com- 
position. As the limestone and shale 

in the plant change in com- 

the proportions required in 

also change. These changes 

are usually accompanied by changes 

in the carbonate content required to 

secure a satisfactory mix composition. 

The carbonate content required at any 
given time to secure a desired com- 
position will be referred to as the 
carbonate requirement. Carbonate de- 
terminations still serve in securing 

the mix 

accurate control of proportions, but 
the value sought must be adjusted 
from time to time to correspond with 
the carbonate requirement. The lab- 
oratory phase of the proportioning 
operation consequently involves two 
problems: to establish relations be- 
tween the various constituents to be 
maintained continuously in the raw 
mix fed to the kilns; and to develop 
principles which may form a basis for 
methods of control in which the ad- 
vantages of the speed and conveni- 
ence of carbonate determinations are 
retained in operations in which the 
principal object is to secure desired 
relations between constituents. The 
first problem will be discussed briefly. 
The second problem involves the de- 
velopment of a method for determin- 
ing the carbonate requirement, which 
is discussed in detail in Part II. The 
application of the principles to be 
brought out is an individual problem 
for each plant, because of differences 
in equipment and layout. To assist in 
planning a system of control suitable 
for a particular plant, application to 
typical processes will be discussed at 
some length in Part III. 

Relations Sought in Compo- 
sition Control 

Since the early days of the industry 
various formulas have been devised 
to express relations to be sought in 
control of compositi n. In some cas< 
these formulas have been empirical, 
while in others the formulas have 
expressed relations based upon 
theories of constitution 
cement clinker, usually 
erally accepted at the 
not the purpose of this paper to dis- 
cuss the history of proportioning for- 
mulas, but to consider composition 
control on the basis of present ideas 
concerning the constitution of port- 
land cement clinker. Although it is 
understood that further research may 
introd uce some modifications,* par- 

♦Since this was written, a paper by M. A. 
Swayze has appeared, in. which is shown tha r 
CjF forms a complete series of lid solutions 
with a new compound, CgA^F. This series in- 
cludes C4AF. It has been found by the writer 
that expression of composition in these terms 
will not affect the formulas in this paper for 
estimating the carbonate requirement, nur the 
methods of control described. Mr. Swayze's 
paper appeared in the American Journal of 
Science, Vol. 244. No. 1. Jan., 1946, and Vol. 
244, No. 2, Feb., 1946. 

of portland 

those gen- 
time. It is 

ticularly with reference to minor con- 
stituents, it may be stated that control 
of composition on the basis of present 
knowledge of the compounds formed 
from the major constituents has led 
to greater uniformity in kiln opera- 
tion and in the quality of the clinker 

The compound composition, calcu- 
lated on the assumption of complete 
combination, will be referred to as the 
potential composition. The following 
equations for calculating potential 
composition will be used in all com- 
putations in this paper. 



4 AF 

4.0710 CaO 

.C024 Si0 2 — 1.4297 Fe 2 3 

7.6024 SiOa + 1-CW 5 Fe L >0 3 + 5.0683 A1 2 3 
2 75 Si ()„> — 0.7544 C3S 
2 04 AM» :: —1.6020 Fe 2 8 
3.0432 Fe 2 Oj 

6.7187 A1 2 3 
-3-0710 CaO 






At the present time the major eon- 

ituents of clinker are believed to be 

mibined in the form of tricalcium 

ilicate, 3CaO # Si02» dicalcium silicate, 

2CaCO*Si< j, tricalcium aluminate, 

34 ►•AI2O3, and tetracalcium alumi- 

noferrite, ACaO'A^CVFesOs. In the 

range of itioi er untered in 

and 1 t clink* magnesia i 

illy ur nibined. The formulas 

foi the 1 rtent npounds may be 

he ( 

A F to repn ent CaO', Al^O 

Si< F , reap In tl 

al I t I, th< formulas of the 

in tl der in which 

thi d above, are I , ( -S, 

I 1 I . ' 

T pen • f the c »ound 

from the ox id» • jni- 
■f a clinke or nt. It i 

1 led 1 , that 

t s of pra* ally identical 

.ion ma 
1 1 may be due 
of minor cot ituents, 

fully nnderafc 1, to the 

ss a a result of rapid 
r to some lack in our present 
kno\K f the reactions of the ma- 

in the clinkering 
1 that the effect of differ- 
en n heat treatment in the kiln is 

r. u Hov. er, the ealcu- 

1. 'tip ition is relat 

jrnabilit f raw mixtures in 
a way that when it is conti led 
v as* b varia^ ns in 

ur : are si 11 and the opera- 

f the k - n turbed. Uni- 

form m| jnd composition 

1 ) unit m kiln o ra- 

1 h nit; m jualit 

It will be observed that in the equa- 
tions for CgS and 1 S the constitu- 
ents derived from limestone and shale 
are of opposite sign, and that the co- 
efficients for CaO, AlijOa, and SiO^ 
are large. It is to be expected, then, 
that a small change in proportions of 
limestone and shale will have a large 
effect upon the potential I S and C L »S. 
An increase of 1.0 per cent in the per- 
centage of lirn cone will increase the 
potential C3S about 12 per cent, and 
reduce the potential CjS about 11.5 
per cent. The 0.5 per cent change in 

the total ( S and Cjfi La dif ibuted 

Nig tl other constituents, « A, 

4 AF, and Mg() r witb only small 

than, jo each. Thus it is n that 

>ntrol of potential C : <S or I 3 i* in 
]) riant, particularly since it is known 
that an increase i - K with a COXTl 

ponding deci e in C2S makes the 
mix more difficult to burn in the kiln. 

It may be mentioned further that the 

etical In limit is attained when 

the potential < .S is redu / 

From this it is easy to understand 
why the crude proportioning process- 
es in the earl days of the y 
frequently led to periods in which the 
product was un and. The trend m 
I ears toward higher I jS m- 
p itions, to in ease e ly streng 
makes fine control -n 
much more important than it was 
twenty years ago. 

Since at most plants the sum of the 

potential C3S and r la near! 

nstant, it is usually unimp rtant 
wh« r a >nstant • S or C : is 
sought. If the raw matt iaii vary in 

such a way that t sum of tht I 
sil ates \arieh rably, ai the 

is brought too low t roes when 

ontrolling on the basis of ; Lential 


C3S, it is a safer practice to seek a 
constant potential C2S. Some opera- 
tors prefer to maintain a constant 
C3S/C2S ratio. This offers no particu- 
lar advantage when the sum of the 
silicates is fairly constant. When the 
sum of the silicates is variable, con- 
trol of the C3S/C2S ratio is a safer 
practice than control of potential C3S 
content. It amounts to a compromise 
between control of potential C3S and 
control of potential C2S. 

An Outline of the Plan of Attack 

Before entering into a detailed study 
of the methods of determining the 
carbonate requirement and applica- 
tions to typical processes, it is desir- 
able to obtain a view of the general 
features of the procedure to be de- 
scribed. In controlling proportions of 
raw materials, the chemist decides 
upon a carbonate content to be main- 
tained in the mix until conditions 
indicate the need of a change, when 
a higher or lower carbonate content 
is selected. The value selected as a 
basis for controlling proportions will 
be referred to as the holding point, 
which is a term used in some cement 
plants. The general plan is to adjust 
the holding point so that it will fol- 
low changes in the carbcnate require- 
ment. This can be accomplished by 
determining the carbonate require- 
ment once a day, or perhaps twice a 
day if it is found to be necessary. 
Through these determinations of the 
carbonate requirement and the corre- 
sponding adjustments of the holding 
point, the advantages of the speed 
and convenience of controlling propor- 
tions by carbonate determinations is 
retained in control operations for 
maintaining a constant potential C3S 

or c 2 s. 

For the determination of the car- 
bonate requirement, to be described 
later, a sample of the raw mix is 
analyzed, determining S1O2, Fe203, 
AI2O3, CaO, and ignition loss. The 
carbonate content is also determined 
by the rapid control method. This de- 
termination requires several hours, 
even with the most rapid analytical 
methods. It should be evident, then, 
that if the limestone and shale change 
in composition abruptly, determina- 
tions of the carbonate requirement 
will serve no useful purpose. To se- 

cure good control of the proportioning 
operation the changes in raw material 
composition must be gradual, either 
naturally or through handling the 
raw materials in such a manner as to 
eliminate abrupt variations. 

Definitions of Terms 

Certain of the terms already men- 
tioned, and others, will be used re- 
peatedly in the discussion which fol- 
lows. Some of these will be used in a 
more general sense, others in a more 
restricted sense, than that in which 
they are commonly understood. They 
are defined here in the sense in which 
they are used in this paper. 

Limestone and Shale. Cement raw 
mixtures are composed principally, 
sometimes entirely, of calcareous and 
argillaceous materials. The calcareous 
material may be limestone, marl, oys- 
ter shells, etc. All these materials, 
used as a source of CaO, will be re- 
ferred to as limestone. Similarly, the 
argillaceous material, supplying both 
SiO«j and A1 2 3 , and usually Fe^Oa, 
may be clay or shale. Such materials 
will be referred to as shale. These 
materials may be combined in nature 
in a single raw material, cement rock. 
Methods referring to limestone and 
shale apply also to cement rock. On 
the other hand, blast furnace slag, 
which supplies both calcareous and 
argillaceous constituents, offers spe- 
cial problems in control of composi- 
tion which are not considered in this 

Iron Ore. Any material which is 
used as a source of Fe20s, such as 
iron ore, pyrites cinders, mill scale, 
etc., will be referred to as iron ore. 

Sand. Any material added to the 
mix to increase the SiOo content will 
be referred to as sand. 

Carbonates. The acid-neutralizing 
value of the mix, or the amount of 
CO2 evolved by the mix in acid, is 
expressed as a percentage of CaCOa. 
This will be referred to as the 
carbonate content, and is equal to 

CaC0 3 + 1.19 MgC0 3 , as previously 
explained. It includes MgCO ;i ex- 
pressed as CaCOs. 

Carbonate Requirement. The car- 
bonate content which the raw mix 
should have to secure a desired po- 
tential C3S or CoS content. 

Holding Paint. The carbonate con- 


tent selected by the plant chemist as 
the value to be maintained in the mix. 
The holding point may be changed 
from time to time, as indicated by 
changes in the carbonate requirement. 

('<> Aete Aval is. Analyses of raw 
mixtures are referred to as "complete 
analyses" if they include SiO_>, Fe-0 ;; , 
AID:, CaO, and ignition loss. 

Lag in C itrol The delay in adjust- 
ment proportions due to the time 
elaj tig between proportioning the 

tterials and the determination of 

arl nate content. For example, this 

will include the time required for ma- 

t< al to pass from the proportioning 

point to the sampling point, the sam- 

ing interval, and the time required 

for i arbonate determination. 

}>, r,/ Raw Mixtures. Mix- 

tures approaching the desired raw 
mix composition, prepared for use in 
a second proportioning operation. 
Since a second proportioning opera- 
tion is seldom used in the dry process, 
preliminary mixtures are usually in 
the form of a raw mix ground with 
water, commonly referred to as a 

Potential C3S or C> 2 S. The value ob- 
tained by applying equation 1 or 2 to 
the composition of a clinker, raw mix 
or raw material, expressed on an ig- 
nited basis. In the case of a raw ma- 
terial, such as limestone or shale, the 
calculated value may be several hun- 
dred per cent, and may be positive or 
negative. The value obtained is used 
in computations as though such per- 
centages could actually be present. 

Part- || — Mathematical Study of the Problem 


HI &RBONATE CONTEN1 of the law 

d on a raw, 01 un- 

igni 1 ;, , while the potential 

• n is exjir d on an ignited 
As the carbonate content i 

adji by changing the proportions 

1 ne and shale, the ignition 

It is evident, then, 
tl relation \ the carbon- 

ate 1 tent of a raw mix and its po- 
mp an is not linear. How 
r, \ thill the narrow range of 
om posit in Ived in prelin ^ai 
:t\\ nxtures, the relation i: o near- 
ir that the effect of changes in 

• t on jjoi tial com- 
p >n can be ex pre ed in ver 

simple terms. This is also true of the 
relation between the percentage of 
limestone or shale and the potential 

Because of the practically linear re- 
lations involved, it is possible to start 
with a single limestone and shale, and 
a single mixture of them, and then 
study the effect of changes in propor- 
tions of the materials upon the car- 
bonate content and upon the potential 
composition. Upon learning these ef- 
fects we can devise a method of esti- 
mating the carbonate requirement. 

For our purpose we can start with 
limestone A f shale, and raw mix No. 
1, which were used previously in illus- 



I ■ . A Shale 

Mix 1 

Mix M 

Differ« t 

Prop loni of Raw Material* 

Linn 4 

Oxide ( ition (Uniffni 



84. 11 


+ 1.17 
J 11 


Ch »rjat.e* 

1 U 
1 l r 
1.64 5.82 

< 1 2.12 
1.20 1-12 

42.35 12.42 

91J19 < 

Potential Composition* 











\ 1 00 


• - 

M g-O 


66.4 r , 






-f 14 
—18 64 






na 1-4 from *h 

ed baaU. 


trating the function of control tests 
in proportioning raw mixtures. To 
demonstrate the effect of increasing 
the carbonate content 1.00 per cent; 
that is, from 77.24 to 78.24 per cent, 
we have calculated another mixture, 
No. 1A, which is shown with mix No. 
1 in the preceding table. 

Referring to the table, it is seen 
that an increase of 1.00 per cent in 
carbonate content increases the C3S 
14.22 per cent and lowers the C2S 
13.54 per cent. This refers to the par- 
ticular raw materials used in making 
mixtures 1 and 1A, but it is typical 
of the results obtained in such compu- 
tations with a wide variety of raw 
materials. In general, the increase in 
C3S for a 1.00 per cent increase in 
carbonate content is approximately 
14.5 per cent, and the decrease in C2S 
about 13.5 per cent. Conversely, to 
obtain an increase of 1.0 per cent in 
potential C3S, the carbonate content 
should be increased 1/14.5, or 0.07 per 
cent. To obtain an increase of 1.0 per 
cent in C2S, the carbonate content 
should be decreased 1/13.5, or 0.074 
per cent. 

Calculation of the Carbonate 


Since the change in carbonate con- 
tent required to secure a 1.0 per cent 
increase in C3S or C2S is known, it is 
possible to calculate the carbonate re- 
quirement from the potential C3S or 
C 2 S content of a raw mix sample,* 
and its carbonate content. For ex- 
ample, let us suppose that a sample 
of mix No. 1 has been analyzed for 
determination of the carbonate re- 
quirement, with the results shown in 
the foregoing table. The carbonate 
content and potential C3S are 77.24 
and 56.45 per cent, respectively. If the 
C3S sought in the control operation 
is 60.0 per cent, the C3S content of the 
sample is 3.55 per cent too low. The 
carbonate requirement is then 77.24 
+ 0.07 X 3.55, or 77.49 per cent The 
same result would be obtained if mix 
No. 1A, made from the same raw ma- 
terials, had been sampled and ana- 
lyzed for determination of the car- 
bonate requirement" It .ihould be 
^served that in sampling for deter- 
mination of the carbonate require- 
ment, all that is necessary is -hat the 
sample is composed of the avr mate- 

rials in use at the time. It does not 
need to be a correctly proportioned 
mix. It is important to understand 
this, because it may sometimes be 
possible to secure early information 
concerning the carbonate requirement 
by taking grab samples for the pur- 
pose instead of samples collected by 
a continuous sampler for routine con- 
trol of proportions. 

The method of calculating the car- 
bonate requirement may be expressed 
in equation form, as follows: 

For control of potential O3S: 

p = p + 0.07 (A — a) (5) 

For control of potential C2S: 

P = p + 0.074(& — B) (6) 

in which P = carbonate requirement 

p = carbonate content of 
mix sample (as deter- 
mined by rapid control 
= desired potential C3S 
= potential C3S in mix 

= desired potential C2S 
— potential C2S in mix 
It should be observed that in deter- 
mining the carbonate requirement the 
carbonate content of the mix should 
be obtained by the rapid control meth- 
od. The carbonate requirement is then 
in the same terms, automatically 
compensating for the effect of con- 
stant errors in the control test. For 
example, it will compensate for the 
present of insoluble CaO and MgO 
in the raw materials in use at the 

Influence of Coal Ash 
and Stack Losses 

As the raw mix passes through the 
kiln some of it is picked up by the 
kiln gases and is carried out through 
the stack. This introduces a change 
in composition, because the fine par- 
ticles caught up by the gases flowing 
through the kiln are not of the same 
composition as the raw mix as a 
whole. In addition, when coal is used 
as fuel, the coal ash is deposited to 
some extent with the raw mix in the 





♦The potential C3S or C2S is calculated from 
i complete analysis of the raw mix. The sam- 
ple must be prepared for analysis by treat- 
ment which will make it possible to decompose 
the sample in acid. The preparation of raw 
mix samples is discussed in Aprendix A. 

kiln and is brought forward to the 
burning zone with the raw mix, where 
it becomes a part of the clinker pro- 
duced. As a result of the combined 
effect of coal ash and dust loss, or 
dust loss alone when gas or oil is used, 
the potential composition of the clink- 
er is not identical with that of the 
raw mix fed to the kiln. The C 3 S or 
C2S sought in the mix should there- 
fore be somewhat different from the 
value desired in the clinker. To deter- 
mine what this difference should be, 
the potential compositions of the kiln 
feed and clinker may be compared 
during a period of typical operation. 
At one plant, for example, the C3S 
sought in the mix is 13 per cent high- 
er than the value desired in the clink- 
er, while at another plant it is 6 per 
cent higher. In determining the car- 
bonate requirement, the desired po- 
tential C 3 S or C2S used in the calcu- 
lation should be the value sought in 
the mix, not the value sought in the 

Influence of Changes in 
Limestone Composition 

A detailed study of the influence of 
changes in composition of the raw 
materials is not needed, since control 
of raw mix composition by adjusting 
the holding point to correspond with 
the carbonate requirement takes care 
of the effects of changes in the raw 
materials. However, a brief study of 
the influence of changes in limestone 
composition will serve to demonstrate 
the need for such a system of control. 
It will also provide examples compar- 
ing the calculated carbonate require- 
ment with the carbonate content of 
mixtures calculated from the lime- 
stone and shale compositions to obtain 
a desired C3S content. 

Tables 1 and 2 have been prepared 
for the purpose of comparing compo- 
sitions of raw mixtures obtained from 
shale and various limestones, each a 
modification of limestone A. In Table 
1, these raw mixtures are made to a 
constant carbonate content, and in 
Table 2 to a constant potential C3S 
content. The raw material composi- 
tions in Table 2 are identical with 
those in corresponding columns of 
Table 1, and are repeated for conveni- 
ence in considering raw mix compo- 

sitions with reference to the lime- 
stone used. The tables are presented 
together to facilitate comparison of 
control based upon carbonate content 
with control based upon securing a 
constant potential C3S. 

The modifications in limestone A to 
obtain the remaining limestones in 
Tables 1 and 2 are as follows: In 
limestone B, CaCC>3 has been replaced 
by MgCC>3 to an extent sufficient to 
lower the CaO content 1.00 per cent. 
This results in a slightly higher igni- 
tion loss in limestone B. Limestone C 
is identical with limestone A on an 
ignited basis, but has a higher igni- 
tion loss. The compositions of lime- 
stones D and E require no comment. 

In Table 1 each limestone has been 
combined with the shale to obtain a 
mixture with 77.24 per cent carbon- 
ates, the carbonate content of mix 
No. 1. In Table 2 each limestone has 
been combined with the shale to ob- 
tain a mixture with 66.45 per cent 
C3S, the potential C3S content of mix 
No. 1. For the purpose of studying the 
effects of changes in limestone com- 
position it will be assumed that 56.45 
per cent C3S is sought in control of 
composition. Table 1 then indicates 
the variations in potential composi- 
tions to be expected when the lime- 
stone changes from A*to B t A to C, 
etc., if the carbonate content is main- 
tained constant without considering 
the changes in the limestone. On the 
other hand, Table 2 indicates the 
changes which will occur under the 
same conditions if the potential C3S 
is maintained at 56.45 per cent. (The 
values in Table 2 are within 0.10 per 
cent of that value.) 

Considering the change from lime- 
stone A to B t it will be seen that to 
maintain a constant potential C3S the 
carbonate content should be raised 
from 77.24 to 77.88 per cent (mix 
No. 6), an increase of 0.64 per cent. 
If the need for this increase is not 
observed, and the carbonate content 
remains at 77.24 per cent, the C3S 
content drops from 56.45 to 47.44 per 
cent (mix No. 2), that is, a decrease 
of 9.0 per cent. This is due to the fact 
that MgO, expressed as CaC03, is in- 
cluded in the carbonate content, but 
does not enter into the computation 
of C 3 S. That is, the 77.24 per cent 










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carbonate content when limestone B 
is used means less CaO available for 
formation of C 3 S than when limestone 
A is used. It may be noted here that 
at some plants the control test is a 
rapid determination of lime content, 
precipitating the lime as oxalate. In 
that case, magnesia is not included in 
the test value, and the effect of the 
change from limestone A to B is to 
increase the potential C3S about 16 
per cent. It is apparent that with 
either control test, variations in mag- 
nesia content may have considerable 
effect upon burnability of the raw 
mix if the holding point is not adjust- 
ed to take care of the variations when 
they occur. 

It is possible to overcome the effect 
of abrupt variations in magnesia con- 
tent by a method which will be pre- 
sented in another paper. In the pres- 
ent paper it is assumed that changes 
in raw material composition occur 
slowly, either naturally or through 
methods of handling the materials. 
Under these conditions, determination 
of the carbonate requirement once a 
day will lead to appropriate changes 
n the holding point. For example, mix 
No. 2 was obtained by maintaining 
the same carbonate content as mix 
No. 1, and shows what will occur if 
the carbonate requirement is not 
known, and the holding point is con- 
qu< j ntly not adjusted to take care of 
the increase in MgO content. Mix No. 
2 is 50.45-47.44, or 9.0 per cent too 
low in potential C3S. Applying equa- 
tion 5 to mix No. 2, the carbonate re- 
quirement is found to be 77.24 4" 0.07 
X 9.0, or 77.87 per cent. If the lime- 
stone changed in MgO content from 
limestone A to limestone B, a deter- 
mination of the carbonate requirement 
would lead to raising the holding 
p t 17 9.0, or 0.6 per cent. This 
maj by r ef erring to mix No. 

6, Tab!< I which has the desired CsS 

a < -irhonate content 

In lii tone A to 

ea J 1 .00 
er ent ) n?c in : atiye 

pr< " ' - nti 

ry , ♦ r 1 

I f ' eent 

Ni " untain a constant poten- 

tial C3S If the carbonate content 1 

not lowered, as it should be, the po- 
tential C3S increases from 56.45 to 
73.20 per cent (mix No. 3), an in- 
crease of 16.75 per cent. At the same 
time the potential C2S is reduced to 
4.14 per cent, making this a very hard 
burning composition. Changes in ig- 
nition loss may not appear to be a 
common source of error in proportion- 
ing, except in plants using marl, in 
which the per cent of organic matter 
fluctuates considerably. It should be 
noted, however, that moisture which 
may be present is a part of the igni- 
tion loss. From this it is seen that 
failure to dry test samples completely, 
or to the same moisture content, may 
have a disturbing effect upon control 

The carbonate requirement, calcu- 
lated from the compositions of raw 
mixtures in Table 1 are shown below, 
with the carbonate content of mix- 
tures in Table 2 which were obtained 
from the corresponding limestones 
when proportioning on the basis of 
potential C3S. 





































76. B0 

•Calculated by equation &. 

It will be observed that the values ob- 
tained by equation 5 are very close 
to the carbonate content actually re- 
quired for a constant C3S, closer than 
the accuracy obtainable in the carbon- 
ate determination. 

Effect* of Iron Ore or 
Sand Additions on the Carbonate 


In recent years there has been a 
demand for cements with lower C3A 
content, or lower C;jA and C4AF con- 
tent, than can be made from limestone 
and shale, or equivalent materials 
communly available at cement plant 
These cements an used for special 
purposes, such as massive concrei 
construction where low heat of hydr. 
tion is desired and concrete expose 1 
to the attack of sulphate . The pr 
due tion of these ments requir U 
addition of high-iron 1 iliceous ma- 
terial, or both, I the raw mix. F 
convenience, the high-ii and sili 



ceous materials will be referred to as 
iron ore and sand, respectively. 

When iron ore or sand is added to 
a raw mix, the potential C3S is low- 
ered and the potential C 2 S is in- 
creased. Since the addition of lime- 
stone has the opposite effect, the effect 
of the iron ore or sand on either the 
C 3 S or C 2 S may be balanced by adding 
a suitable quantity of limestone. The 
problem, then, . is to determine the 
change in carbonate content when the 
iron ore or sand addition has been 
made to a correctly proportioned mix, 
with sufficient limestone added at the 
same time to leave the potential C3S 
or C2S unchanged. For example, if 
control is based upon maintaining a 
desired potential C3S in the mix, the 
"correctly proportioned mix" has the 
desired potential C 3 S, and its carbon- 
ate content is the carbonate require- 
ment determined before the change 
in proportion of iron ore or sand. 

The effect of a change in proportion 
of iron ore or sand on the carbonate 
requirement may be found from the 
following equation: 


Si(A-Ai) (P2 — p)l (7) * 
S 2 (A 2 — A) J 

in which F 



factor representing the 
increase in carbonate 
requirement for each 
per cent increase in 
iron ore or sand 
C 3 S (or C 2 S) sought 
in control 

carbonate requirement 
(before change in pro- 
portion of iron ore or 

C 3 S (or C 2 S) of iron 
ore or sand 

carbonate content of 
iron ore or sand 
100 — ignition loss of 
iron ore or sand 
C 3 S (or C 2 S) of lime- 

carbonate content of 

100 — ignition loss of 
As indicated above, equation 7 may 
be applied in control to secure a de- 
sired C 2 S. The quantities Ai and A 2 
require some explanation. They are 




V2 - 

S 2 

obtained by applying equation 1 or 2 
to the oxide composition, ignited bas- 
is. Since the materials to which they 
refer are not of portland cement com- 
position, the values obtained appear 
unreasonable. However, they have a 
definite significance in mix computa- 
tions. For example, the C3S value of 
a limestone and a shale may be +375 
and — 645 per cent, respectively. 
These values indicate that a substitu- 
tion of 1.0 per cent limestone in place 
of 1.0 per cent shale, ignited weight 
basis, raises the potential C3S in the 
mix 3.75— (—6.45), or 10.2 per 
cent. Because of their definite signifi- 
cance with reference to the effect 
which they have on the potential C3S 
or C 2 S in raw mixtures, these appar- 
ently unreasonable values of A\ and 
A2 are used in mix computations as 
though they represented real per- 
centages of these compounds. 

Equation 7 is too complex for use 
in routine mix control operations. 
Furthermore, it would be unusual to 
have complete analyses of the lime- 
stone and iron ore or sand in actual 
use at the time that an estimate of 
the change in carbonate requirement 
is needed. We must therefore examine 
the possibility of simplifying the for- 
mula by substituting approximate 
analyses of these materials for anal- 
yses representing accurately the ma- 
terials in use at the time. It might 
seem that this would be impossible in 
the case of limestone, since this is 
present in greatest quantity in the 
mix. However, it should be noted that 
the equation is based on the idea that 
the limestone and iron ore or sand is 


added to a correctly proportioned mix, 
represented by A and p. This takes 
care of the shale and all the limestone 
except that added to balance the iron 
ore or sand. Any error due to differ- 
ences between the average limestone 
composition and the composition of 
the limestone in actual use at the time 
applies only to the comparatively 
small quantity of limestone required 
to balance the^iron ore or sand. From 
these considerations it appears fea- 
sible to simplify equation 7 by sub- 
stituting the desired C3S content for 
A, and substituting values obtained 
from average compositions of lime- 

•Equation 7 is derived in Appendix B. 


stone and iron ore or sand for the 
quantities designated by subscripts. 

Since the simplified formula is 
based upon average compositions of 
limestone and iron ore or shale in use 
at the plant, it is impossible to pre- 
sent a formula here for general use. 
However, the method of deriving such 
a formula may be shown by a specific 
example. Let us assume that at a par- 
ticular plant the average composi- 
tions of the limestone and iron ore are 
those given in the following table. 

Iron Ore Limestone 


SiCh 13.34 3~57 

Al.Oa 5.32 1-53 

Fe-Oi 66-43 1.64 

CaO 4.57 49.71 

MgO 0.79 1.20 

Ignition loss 9.65 42.35 

Carbonates pi = 10.12 po= 91-70 

C 3 S A x = — 236 A 2 = 282 

100 — ignition lose . Si= 90.45 S«= 57.65 

Substituting in equation 7, 

F ~ 

10.12 — p + 

F - 



10.12 — p - 

90.45(50 + 236) (91.70 — p) 
57.65(282 — 50) 

90.45 > 286(91.70 — pi 

F - 1.87 — 0.0293p 

57.65 X 232 


For all values of the carbonate re- 
quirement, p, which are encountered 
in practice, the value of F obtained 
from equation 8 is negative; that is, 
an increase in the proportion of iron 
ore in the mix lowers the carbonate 
requirement, and vice versa. To illus- 
trate the use of equation 8, let us as- 
sume that the carbonate requirement 
is 76.2 per cent and that the propor- 
tion of iron ore is to be reduced from 
3.5 per cent to 1.0 per cent, that is, 
a reduction of 2.5 per cent. The fac- 
tor F is 1.87 — <0.0293 X 76.2), or 
— 0.363. The carbonate requirement 
should therefore be increased 0.363 X 
2.5, or 0.91 per cent, that is, from 
76.2 to 77.1 per cent. 

Simplified formulas, derived in the 
same manner as equation 8, are rea- 
sonably accurate for all changes in 
proportion of iron ore encountered in 
practice. This is a result of the fact 
that large percentages of iron ore are 
not used, and also that the amount of 
limestone required to balance the 
effect of the iron ore is small. It is 
because of the small amount of lime- 
stone required that the value of F is 
negative. On the other hand, sand or 
equivalent material is used in larger 
quantities, and from four to six times 
its weight is needed to balance its 
effect on potential C3S or C2S. Equa- 
tion 7 applies accurately to both iron 
ore or sand, but a simplified equation 
derived from it in the same manner 
as equation 8 is not as accurate in 
the case of sand. It will be satisfac- 
tory for small changes in proportions 
of sand, but should not be applied to 
large changes. The maximum change 
in proportion of sand to which such 
an equation may be applied will de- 
pend upon the extent to which the 
limestone and sand compositions vary 
from the compositions used in deriv- 
ing the equation. The limit cannot 
be established theoretically. However, 
since a sample is taken after the 
change in proportion of sand, for a 
determination of the carbonate re- 
quirement, the maximum change in 
proportion of sand to which the equa- 
tion may be safely applied will be 
learned by observation. 

When both iron ore and sand are 
used, and the proportions of both are 
changed simultaneously, the effects of 
these changes can be estimated sep- 
arately and then combined. For ex- 
ample, if the change in proportion, pf 
sand requires an increase of 1.8 per 
cent in the carbonate requirement, 
and the change in proportion of iron 
ore requires a decrease of 0.7 per 
cent, the net change in the carbonate 
requirement is an increase of 1.8 — 
0.7, or 1.1 per cent. 

Part III — Application to Typical Processes 

A variety of processes are used in 
pieparing raw mixtures for the 
manufacture of portland cement. 
From the standpoint of the procedure 
to be followed in applying determina- 

tions of the carbonate requirement in 
control of raw mix composition, they 
may be classified as follows: 

1. Continuous prop- rtioning proc- 
esses, in which the crushed raw mat«- 



•^Proportioning point 

Sampling point 



Kiln Feed 

Fig. 1: Continuous proportioning process with 

no Wending 

rials move in separate streams toward 
a common point at which they are 
combined into a single stream, as 
shown in the flow diagram, Fig. 1, 
This is the only proportioning opera- 
tion, the remaining operations being 
concerned with reduction of the mix- 
ture to a desired degree of fineness. 
In these processes the raw mix is us- 
ually handled in a dry condition. Con- 
trol # of composition in the single 
proportioning operation is usually 
unsatisfactory, and it has consequent- 
ly become a common practice to blend 
the ground raw mixture, as shown in 
the flow diagram, Fig. 2. The blending 





I Crushing 


roportioning point 


Sampling point 

(intermit tent for proportioning, 
continuous for composite 
somples of silos) 

Silos filled 
consecutive fy 

Rg. 2. 


Kiln Feed 

-Blending silos 

Silos emptied 

Fig. 2: Continuous proportioning process with 


operation, which will be discussed in 
more detail later, smooths out varia- 
tions in composition. 

2. Two-stage proportioning process- 
es. In these processes the first stage 
is a continuous proportioning process 
of the type shown in Fig. 1, The prod- 
uct of this stage is proportioned again 
in a second stage, which is a batch 
process. Only a few dry process plants 
use two-stage proportioning. It is 
commonly used in the wet process, in 
which the raw mixture is ground wet, 
forming a slurry. The flow diagram 
of a typical two-st^ge process is 
shown in Fig. 3. 


I ... 






First proportioning point 


Separation of stream 
info botches 



— Mixing tanks 

Second proportioning poinl 

Kiln Teed Basin 

Fig. 3. 

Fig. 3: Two-stoge process (wet) 

In a few wet process plants having 
mixing tanks of large capacity, sam- 
ples of the entire quantity of slurry 
in a tank are taken at intervals while 
the tank is being filled. The car- 
bonate contents of these samples are 
used as a basis for determining the 
proportions of limestone and shale or 
equivalent materials, at the first pro- 
portioning point (Fig. 3). This proc- 
ess differs from that shown in Fig. 3, 
since the desired carbonate content 
is obtained when each tank is filled, 
so that each mixing tank is also a 
correction tank. Although the actual 
proportioning operation is carried on 
at only one point, the process is equiv- 
alent to a two-stage proportioning 


The Continuous Proportioning 


Because of the difficulty of obtain- 
ing representative samples of raw 
mixtures in the crushed state, samples 
for control of the proportioning oper- 
ation are taken from the discharge 
of the grinding mills, as shown in Fig. 
1 and 2. As a result, the sample does 
not necessarily represent the product 
of the proportioning operation at the 
time the sample was taken, but repre- 
sents the conditions at the proportion- 
ing point at an earlier time. By the 
time that the carbonate content of 
the sample is reported, the raw mix 
which it represents has passed on to 
the blending silos, and raw mix which 
has been proportioned later than the 
mix represented by the sample has 
passed into the feed bins for the 
grinding mills. This constitutes a 
"lag" in control, and this lag was the 
ource of much of the difficulty in 
aw mix control in the early years of 
the industry. When there were abrupt 
variations in composition of the raw 
materials the effects of tin \ varia- 
tions were not observed until a con- 
siderable quantity of incorrectly pro- 
j tioned material had passed from 
the proportioning point into the sys- 
tem, with no further opportunity for 
correction. In m< rn installatii ns the 
lag in control is reduced, or the effects 
of lap are reduced to such an extent 
as to be negligible. 

The lap in control may be reduced 
by reducing the capacity of feed bins 
for the grinding mills. The type cf 
grinding equipment may also play a 
part in increasing or decreasing the 
lag in control. At some plants in 
which a large number of mills are 
used, the operation of one of the mills 
is conducted in such a manner as to 
reduce the lag, for sampling, while 
the remaining mills are operating on 
the same material without reference 
to reducing the lag. 

Reduction of the Effect of Lag in 
Control. Assuming that the propor- 
tioning equipment is reliable, the ef- 
fect of lag in control is due to varia- 
tions in composition of the raw 
materials; that is, a change in com- 
position of the raw materials may 
alter the carbonate content of the mix 
at the proportioning point. However, 

because of the lag in control, the need 
of a change in proportions is not 
known for some time. The condition 
is not remedied by improving the pro- 
portioning equipment, but it may be 
improved by handling the separate 
raw materials in such a manner as to 
smooth out variations in composition. 
For example, the limestone storage 
bin may be filled in successive layers 
at the angle of repose. If the lime- 
stone is drawn simultaneously from 
a series of openings along the bottom, 
the effect is to average the limestone 
mechanically, smoothing out varia- 
tions in all the constituents present. 
This procedure not only smooths out 
the variations in carbonate content, 
but also smooths out variations in the 
carbonate requirement. As a result, 
it practically eliminates one of the 
greatest sources of difficulty in con- 
trolling the carbonate content with 
reference to the holding point, and 
also makes it possible to use deter- 
minations of the carbonate require- 
ment effectively in setting the holding 


If only one raw material is blended 
by an operation such as that described 
above, the limestone is the better 
choice, since in most instances varia- 
tions in limestone composition disturb 
control of potential C3S and C2S to a 
greater extent than variations in 
shale composition. Plants which have 
adopted limestone blending have found 
that control of raw mix composition 
has been greatly improved. 

Blending Ground Raw Mixtures. 

When dry raw mixtures are fed into 
a silo, and then drawn from the bot- 
tom, the mix as drawn varies in com- 
position in about the same way as the 
material fed into the silo. Very little 
blending occurs. To secure a blending 
effect, the scheme shown in Fig. 2 i 
commonly used. That is, the silos are 
filled consecutively and emptied simul- 
taneously. At any given time the ma- 
terial drawn from the silos is a mix- 
ture of materials proportioned at 
widely different times. This contitutes 
a mechanical averaging, tending to 
smooth out variations in composition. 
In considering the blending effect ob- 
tainable from a group of silos it is 
necessary to consider composition var- 
iations of two kinds: (1) short swing 


variations, occurring at intervals 
which are short in comparison with 
the time required to fill a silo, and (2) 
long swing variations, which occur 
during a considerable period of time. 
The blending operation smooths out 
both short and lon£ swing variations, 
but in a different manner. Formulas 
for estimating the blending effect ob- 
tainable from a given number of silos 
may be misapplied if this difference is 
not understood. 

In applying the mathematical the- 
ory of probabilities to problems of 
this kind, it is convenient to express 
the variability in composition in terms 
of standard deviation. Let us suppose 
than N silos are being filled consecu- 
tively and emptied simultaneously. 
The carbonate content of the entering 
stream varies in short swings, but 
there is no difference in the average 
composition in the individual silos, 
since a constant holding point has 
been maintained. In that case the 
standard deviation of the material 
drawn from the silos will be equal to 
the standard deviation of the entering 
stream divided by y/N. 

In this study we are concerned with 
the changes to be made in the holding 
point to maintain a ctnstant poten- 
tial C3S or C2S content, within rea- 
sonable limits. If the holding point is 
changed between silo fillings, these 
changes may be regarded as long 
swing variations. The silos differ in 
average carbonate content, and each 
is subject to short swing variations. 
If the previous method of estimating 
the blending effect is applied to the 
deviations from the general average 
for the contents of all the silos, a cor- 
rect estimate of the blending effect 
will not be obtained. Instead, the devi- 
ations of the stream entering each 
silo should be the deviations from the 
average for that silo. Assuming that 
there are N silos, with the standard 
deviations identical, the standard de- 
viation of the material drawn from 
all thfe silos simultaneously will be 
the standard deviation obtained in 
this manner, divided by viV. 

This principle is important in its 
bearing upon a method of control to 
be described presently, and so we pro- 
pose to emphasize it by an example in 
which the materials in the silos are 
widely different in composition. Let 

us suppose that two silos are filled, 
one with material containing 85 per 
cent carbonates, the other 65 per cent, 
so that the average is 75 per cent. The 
standard deviation during the filling 
is assumed in each case to be 0.7 per 
cent, determined from the deviations 
from 85 and 65 per cent, respectively. 
The stream drawn from the silos si- 
multaneously will contain 75 per cent 
carbonates, with a standard deviation 
of 0.7/ v 2, or about 0.5 per cent. In 
view of the wide difference in carbon- 
ate content for the two silos, it must 
be assumed that they are drawn at 
such uniform rates that further devi- 
ations are not introduced in this op- 
eration. It may be seen from this ex- 
treme case that it would be absurd 
to measure deviations in the stream 
entering the individual silos from the 
general average, 75 per cent, for the 
two silos. 

From the principles discussed, it is 
evident that blending after propor- 
tioning has limitations. Nine silos 
would be required to reduce varia- 
tions to a third of the original varia- 
tions, and sixteen silos to reduce them 
to a fourth. It may be of interest to 
note that eight silos would suffice in 
the latter case, if the blended mate- 
rial from four silos is blended again 
in the other four. 

Other methods, such as circulation 
of material in the blending silos, and 
the introduction of air through porous 
plates at the bottom of the silo to give 
the dry mix the flow characteristics 
of a liquid, are sometimes used. 

Due to limitations of the blending 

which may be accomplished, it is im- 
portant that proportioning before 
blending should be sufficiently accu- 
rate to result in satisfactory uniform- 
ity in the blended product. In some 
instances blending silos have been in- 
stalled with the idea that they will 
eliminate variations in raw mix com- 
positions to a greater extent than is 
possible. In that case, the results are 
disappointing, and it then become 
necessary to use the blending silos as 
storage silos for a second proportion- 
ing operation; that is, when it is nec- 
essary to select pairs of silos to supply 
high- and low-lime mixtures to be 
combined to form a desired mix, the 
silos are net blending silos, but are 
used as sources of material for a sec- 


ond proportioning operation. 

In practice, the blending operation 
is con .uous. That is, the filling and 
emptying of the silos are going en si- 
multaneously. To secure the greatest 
blending effect, as many silos as pos- 
sible should be drawn at one time 
The blending effect of eight silos can- 
not* be obte ed if only four are 
drawn at a ne. 

In describing the blending opera- 
tion it was assumed f:r the purpose 
of illustration that the purpose in 
control is to maintain a constant car- 
bonate content and that the blending 
operation smooths out deviations from 
at ; ant value. However, if the 
arl late requirement changes, the 
olding point should be changed ac- 
cording If the carbonate content is 
maintained reasonably close to the 
carbonate requirement the mix drawn 
from the blending silos may vary in 
carbonate content to a greater extent 
nan when the holding: point is no- 
change from time to time. However, 
he de or the _arbonate re- 

quirem : will be reduced by the 
blending operation. 

Two M of b .ding operation 

have been considered: (1) blending 
-jar ate raw materials; and (2) 
blending the ground raw mix. The 
principle is the st e, but e purpose 
is different. The first operaticn is in- 
tended to improve control of compo- 
s on in the proportioning operation. 
The object of the second cperation is 
o smooth out errors in proportioning 
af they have occurred. Both types 
may be employe to advantage. 

Sampling for Control of the Pro- 
portioning Operation. The lag in con- 
trol ould be taken into account in 
judging the significance of tests on 
samples of the ground raw mix; that 
is, it should be borne in mind that the 
sample does net represent the propor- 
tioning operation at the time, but at 
a previous time. For example, if the 
tin between proportioning and sam- 
pling is three hours, a sample taken 
at the mill discharge represents the 
condition at the proportioning point 
three hours earlier. If samples are 
collected from a continuous sampler 
at two-hour intervals, the sample rep- 
reser the average condition at the 
proportioning point during a period 
between three and five hours earlier 

than the time at which the sample is 
collected. The time intervals men- 
tioned are not intended to represent 
plant practice, but serve to illustrate 
the importance of reducing the lag in 
contra] by collecting samples inter- 
mittently, rather than continuously, 
for a check on the proportioning op- 
eration. rWfa applies particularly to 
continuous proportioning processes. 
Samples may be collected ccntinuous- 
ly for other purposes, for example, to 
obtain a composite sample of the raw 
mix in a silo or tank while it is being 


Selection of Holding Points in a 
Continuous Proportioning Process. It 
was pointed out previously that blend- 
ing silor for'ground raw mixtures do 
not eliminate short swing variations 
in composition but merely reduce them 
to a fraction of the deviatiens in the 
stream entering the silos. On the oth- 
er hand, long swing variations caused 
by changes in the holding point are 
almost completely eliminated. This 
provides a basis for two methods of 
contrclling the potential C3S or G2S 
content. In the first method to be con- 
sidered, the approach to the carbonate 
requirement is in the proportioning 
operation, through determinations of 
the carbonate requirement daily, cr 
twice a day if necessary, and adjust- 
ment of the holding point to corre- 
spond with it. In this method, efforts 
are in the direction of maintaining a 
carbonate content close to the carbon- 
ate requirement before the blending 
operation. In the alternate method, to 
be described presently, the approach 
to the carbonate requirement is in the 
blending operation. 

In the first method, in' which the 
approach to the carbonate require- 
ment is in the proportioning opera- 
tion, the holding point is adjusted to 
correspond with the carbonate re- 
quirement. In discussing the proced- 
ure it will be assumed that the raw 
materials vary slowly in composition, 
either naturally or through the man- 
ner in which they are handled. In that 
case, the carbonate requirement will 
vary slowly, so that the high and low 
points are several days apart. In the 
periods between these points the car- 
bonate requirement is steadily in- 
creasing or decreasing Such trends 
fihnnlH he observed, and holdine point* 


selected to follow these trends. Sup- 
pose, for example, that the carbonate 
requirement is reported on successive 
days as 76.5, 75.7 and 75.0 per cent. 
If these values are selected as holding 
points on the three days, the carbon- 
ate content will be the same as the 
carbonate requirement at the begin- 
ning of each day, but will exceed it 
for the remainder of the day. If there 
is an upward or downward trend in 
the carbonate requirement, the hold- 
ing point should be adjusted from 
time to time during the day, to follow 
the trend. 

In following the trend of the car- 
bonate requirement, it should be borne 
in mind that the value reported is not 
the value at the time of reporting, but 
refers to an earlier time. For example, 
the sample used for the determination 
may represent material proportioned 
five or six hours before the report. If 
the carbonate requirement is plotted 
against time, as a means of following 
the trend, it should refer to the esti- 
mated time of proportioning. During 
periods in which the trend is definitely 
downward or upward, the holding 
points can be kept quite close to the 
carbonate requirement. However, with 
the value determined only once a day, 
it may be difficult to judge when a 
high or low point is approached. It is 
at these times that the holding point 
may fail to approach the carbonate 
requirement as closely as may be de- 
sired. With adequate blending facili- 
ties these deviations can be reduced 
to such an extent that they are negli- 

Alternate Method. When the car- 
bonate requirement varies too rapidly 
to permit satisfactory estimates of the 
trend in the carbonate requirement it 
is necessary to adopt a method in 
which these estimates are not needed. 
The alternate method now to be de- 
scribed is based upon the fact that 
when adequate blending of the raw 
mix is provided it is only necessary 
that the average carbonate content 
should coincide with the average car- 
bonate requirement. It should be un- 
derstood that these averages refer to 
the total quantity of raw mix in the 
series of blending silos at any given 
time. When this condition is main- 
tained, the function of the blending 
operation is to smooth out the short 

swing variations in the difference be- 
tween the carbonate content and the 
carbonate" requirement. The method 
is described as follows. 

Samples are taken at regular inter- 
vals at the sampling point shown in 
Fig. 2, for controlling operations at 
the proportioning point. At the same 
time a continuous sampling device is 
in operation to secure a composite 
sample of the stream discharged into 
each silo. When a silo is filled, the 
composite sample is used for deter- 
mination "of the average carbonate 
content and the average carbonate re- 
quirement of the silo contents. The 
difference between these values is the 
excess or deficiency of carbonates, as 
compared with the carbonate require- 

Following this procedure for each 
silo, a record of the excess or defici- 
ency in each silo may be kept, with the 
accumulative total in another column. 
In calculating the accumulative total 
any excess is added, and any defici- 
ency subtracted. By selecting holding 
points to maintain the excess or de- 
ficiency of carbonates in the accumu- 
lative total as close to zero as possible, 
the proportioning operation is con- 
trolled to produce at most only a 
negligible excess or deficiency in the 
average composition of the entire se- 
ries of silos. The carbonate content of 
the finished raw mix may vary, but 
these variations will for the most 
part be due to variations in the car- 
bonate requirement, and are there- 
fore not a matter of concern. 

Blending silos frequently differ in 
capacity. The interstices between cir- 
cular silos are commonly used, and 
these are of much smaller capacity 
than the circular silos. In such cases 
the excess or deficiency in each silo 
should be expressed in pounds, bar- 
rels or tons. For example, if a silo 
contains 1000 tons of raw mix, and 
the excess of carbonates is 1.3 per 
cent, this is equivalent to 1000 X 
0.013, or 13 tons excess carbonates. 

The Two-Stage Proportioning 


In the two-stage process the first 
stage is a continuous proportioning 
process supplying tanks of slurry to 


be proportioned in batches in the sec- 
ond stage. At seme plants the first 
proportioning operation is performed 
roughly, with no effort to produce pre- 
liminary mixtures close to the desired 
composition, while at others weighing 
devices are used to obtain fairly accu- 
rate control. In either case the desired 
composition can be obtained in the 
slurry fed to the kilns, but there is a 
difference in the degree of accuracy 
required in the second stage. If the 
preliminary raw mixtures (slurries) 
are close to the desired composition, 
the effects of errors in percentages of 
the slurries in the final mixtures are 
small. On the other hand, rough pro- 
portioning in the first stage introduc- 
es the necessity of accuracy in the 
second stage. In describing methods 
this difference in conditions will be 

In most instances slurry tanks must 
be released for the proportioning op- 
eration too rapidly to permit complete 
analysis of each tank of slurry. The 
second proportioning operation is con- 
sequently an operation for control of 
the carbonate content. If the carbon- 
ate requirement is determined at suit- 
able intervals, and the holding point 
selected accordingly, the potential C3S 
or C L >S is controlled within reasonable 
limits. Some plants have a sufficient 
number of tanks to permit complete 
analysis of each tank before release. 
Under these conditions potential com- 
position is under direct control. Meth- 
ods of performing the necessary com- 
putations for this type of operation 
are described in Part IV. In this sec- 
tion it will be assumed that complete 
analyses of the individual tanks of 
slurry are not available. 

Computation of proportions of slur- 
ry to obtain a desired carbonate con- 
tent is not difficult. To illustrate, let 
us assume that the test values for 
two tanks of slurry are as indicated 

below, and that the holding point is 
73.2 per cent carbonates. 



No. 1 

No. 2 

Total carbonates 




Per cent moisture . 



Deviation from 

. . +12.4 


On the last line the deviations from 
the holding point are shown. These 
values, taken in reverse order, repre- 
sent the relative proportions of slur- 
ry, on a dry weight basis, required to 
obtain 73.2 per cent carbonates in the 
mixture. That is, 5.0 parts by weight 
of slurry No. 1 and 12.4 parts by 
weight of slurry No. 2, dry weight 
basis, will give the required composi- 
tion. These may be converted to a 
relative slurry volume basis by multi- 
plying each of these relative weights 
by a factor obtained from Table 3. In 
these cases the relative volumes are 
obtained as follows: 

Rel wt., Factor 
dry basis (Table 3) 
Slurry No. 1 5.0 X 1.10 = 
Slurry No. 2 12.4 X 1.31 = 


Let us suppose that the tanks are 
of the same diameter and that the 
depth of available slurry in each is 
30 ft. Since slurry No. 2 is used in 
greater quantity, the entire 30 ft. 
may be used to empty the tank for 
further operations. The number of 
feet of slurry to be drawn from tank 
No. 1 is found as follows: 

30 X 5.50 

10.16 ft., or 10 ft, 2 in. 

Considering the preliminary raw 
mixtures on a dry basis, the effect of 
errors in proportions is proportional 
to the difference between the carbon- 
ate contents of the two materials. In 
this case the difference is 85.6 — 68.2, 
or 17.4 per cent. It will be noted that 
this is the same as the sum of the 
relative weights, as obtained directly 
from the deviations from the desired 
carbonate content. An error of 1.0 
per cent in proportions of the two 
materials will cause an error of 0.174 
per cent in the carbonate content of 
the mixture. For example, the per- 
centages of slurries No. 1 and 2 on a 
dry basis are 100 X 5.0/17.4 and 100 
X 12.4/17.4, or 28.74 and 71.26 per 
cent, respectively. If the actual 
amounts used are 29.74 and 70.26 per 
cent, the carbonate content of the mix 
will be 73.2 + 0.17, or 73.37 per cent. 
From this it may be seen that accu- 
racy in measuring slurry volumes is 
required to control the carbonate con- 
tent within 0.2 per cent. Because of 


the physical condition of raw mix 
slurry, it is difficult to measure vol- 
umes with a high degree of accuracy. 
It is therefore good practice to test 
the mixture for carbonate content, 
and to make such adjustments as may 

be required. The calculation of quan- 
tities is therefore intended only to 
secure an approximation to the de- 
sired composition. 

When the slurries to be combined 
are close to the desired composition, 
the effect of errors in proportioning 
are comparatively small. For exam- 
ple, if cne slurry is 2.0 per cent too 
high in carbonate content, and the 
other 2.0 per cent too low, the sum 
of the deviations is 4.0 per cent. An 
error of 1.0 per cent in proportions 
of the two slurries, on a dry weight 
basis, will introduce an error of only 
0.04 per cent in the carbonate con- 
tent of the mixture. In such cases it 
may be possible to combine the slur- 
ries in the calculated quantities, with- 

out depending upon further adjust-^ 
ments based on determinations of the 
carbonate content of the mixture. If 
the moisture contents of the slurries 
are not far apart, the relative pro- 
portions on a dry basis may be taken 
also as relative proportions on a vol- 
ume basis, -without applying the fac- 
tors in Table 3. These are advantages 
secured by accurate proportioning in 
the first stage. 

It may be noted that in Table 3 
it is assumed that the specific gravity 
of the dry raw mix is 2.65. This is an 
estimate, but does not necessarily fit 
every case. In addition, the accuracy 
of the conversion is impaired by the 
presence of entrained air in the slurry* 
However, if the calculated quantities 
of slurry are regarded as approxi- 
mate, to be checked when necessary 
by tests of the mixtures of slurry, 
the factors may be regarded as being 
generally applicable. 





DRY 7 













































































































































































































































♦The specific gravity of the dried slurry is assumed to be 2.65, and the slurry is assumed 
to contain no entrained air. Since the specific gravity of individual dried slurries may de- 
part from 2.65, and entrained air is usually present in slurry in variable amounts, the 
factors in the table must be considered as approximate values and are therefore expressed 
only to two decimal places. 

The table is based upon the equation. 

Factor ■=. 

fctlOO + id— l)w] 
d(l0Q — w) 

iv which d = specific gravity of dried slurry 

w = per cent moisture 

k = arbitrary constant 
Assuming d == 2.65, and selecting 1.272 as a value of k which will make the factor for 30 
per cent moisture slightly greater than 1.00. the equation reduces to the form, 

Factor = 

48 -I- 0.792«? 




p or t IV — Direct Control of Potentiol Composition 

The foregoing study of proportion- 
ing methods is concerned with the 
problem of controlling potential com- 
position in processes in which there 
is no opportunity for calculating pro- 
portions of materials from complete 
analyses. Complete analyses are re- 
quired in determining the carbonate 
requirement, but are not completed 
in time for direct application to 
specific problems. However, it has been 
shown that they can serve a useful 
purpose if changes in the carbonate 
requirement occur slowly. 

When a complete analysis of each 
tank of slurry can be made before 
the slurry is released, combinations 
of slurries can be made in proportions 
calculated from the complete analyses. 
This constitutes direct control of po- 
tential composition. 

desired potential C 3 S, ifi this case 
assumed to be 60 per cent. 

Deviations of the potential C3S 
from the desired value, 60 per cent, 
are shown on the last line pf the table. 
These values are converted to an un- 
ignited basis by multiplying by (100 
loss)/100. For example, the ignition 
loss of slurry No. 1 is 38.21 per cent. 
The C 3 S deviation on an unignited 
basis is 35.6 X 0.6179, or 22.0 per cent. 

Taken in reverse order, the C3S 
deviations, on an unignited basis, rep- 
resent relative weights of the slur- 
ries, dry basis, required for a mixture 
with the desired 60 per cent potential 
C 3 S; that is, 45.8 parts by weight 
of slurry No. 1 and 22.0 parts by 
weight of slurry No. 2, each on a dry 
weight basis, will form a mixture of 
the desired composition. These rela- 

No. 1 

ted basis 

No. 2 

Unignited (dry) basis 
No. 1 No. 2 

Wet basis 
No. 1 No. 2 




At G 3 

Ft 3 



Ignition loss 






78.9 72.6 
38.21 35.56 

32.3 87.1 

Calculated Values 

Pocntial C-S** 95.6 
C3S deviation +35.6 

*By rapid control method. 
•♦Calculated by equation 1, 

— 11.1 

— 71.1 

+ 22.0 —45.8 

In discussing the indirect method, 
based upon determinations of the car- 
bonate requirement at regular inter- 
vals, it was emphasized that it can be 
applied only when changes in the car- 
bonate requirement occur slowly. The 
direct method is not subject to this 
conditicn. Since each combination of 
slurries is made on the basis of com- 
plete analyses, abrupt variations in 
the composition of the raw materials 
do not interfere with^control of po- 
tential C 3 S or Q>S. In addition, there 
is the possibility of controlling more 
than one constituent, as will be shown. 

Control of One Constituent 

The following data for two tanks 
of slurry, No, 1 and 2, will be used 
in illustrating methods cf estimating 
proportions of slurries to obtain a 

tive weights are used in estimating 
the relative volumes of slurry required 
and the carbonate content of the mix- 
ture, as will now be shown. 


Per cent 





No. 1 
No. 2 







Relative volumes of slurry are ob- 
tained by multiplying each relative 
weight, dry basis, by a factor obtained 
from Table 3. The computations in 
this case are shown above. 

From these relative volumes the num- 
ber of feet of slurry in tanks of the 
same diameter can be calculated. For 
example, if 30 ft. of slurry No. 1 is 
used, the required quantity of slurry 
No. 2 is 30 X 27.1/49.9, or 16.3 ft. 


The carbonate content of the mix- 
ture may be calculated as indicated 



weights Carbonate 
(unignited) Content 

No. 1 
No. 2 

45.8 X 78.9 = 
22.0 X 72.6 =: 






Carbonate content = 



= 76.9% 

It is good practice to determine the 
carbonate content of the mixture, to 
test the accuracy with which the 
proportioning has been accomplished. 
In this case, the carbonate content 
should be 7G.9 per cent. If the value 
obtained differs from this value to a 
greater extent than is considered al- 
lowable, an adjustment should be 
made. In deciding upen the degree of 
accuracy required in this adjustment 
it should be borne in mind that each 
0/1 per cent deviation in the carbon- 
ate content is equivalent to a deviation 
of about 1.4 per cent in potential C 3 S. 

Graphic Method. The proportions of 
slurries, on a dry weight basis, re- 
quired to obtain a desired potential 
C3S or C L >S, and the carbonate con- 
tent of the mixture, may be deter- 
mined graphically. This is illustrated 
in Fig. 4 for the foregoing problem. 
The C3S deviation, unignited basis, 
and the carbonate content of each 
slurry are plotted in the figure as 
indicated at the points designated a 
slurries No. 1 and 2. For exanip e, 
the p dnt for slurry No. 1 is located 
at 22.0 per cent C ;J S deviation and 

78,9 per cent carbonates. The line 
joining these points is divided into 

two segments by the vertical line rep- 
resenting zero C3S deviation. The 
lengths of these segments represent 
the relative weights of the two slur- 
ris, dry basis, required to obtain tb 
desired potential C3S. The segment 
farthest from the point for either 
slurry represents the relative weight 
of that slurry, as indicated in Fig, 4. 
In this figure only 10 per cent inter- 
vals for Cs.S deviations and two per 
cent intervals for carbonate content 
are shown, but for accuracy in locat- 
ing points and in measurements a 
sheet of graph paper is used. In the 
original graph from which the figure 
is drawn, the lengths of the segment 
are 10.1 and 4 » in. These ai the 
relative weights of slurries No. 1 and 
No. 2, respectively, on a dry basis. 

The line joining the t 1 slurries in 
Fig. 4 intersects the vertical zero C3S 
deviation line at 76.9 per cent car- 
bonates, which is the carbonate con- 
tent of the mixture. 

The relative wei ts of slurry, on 
a dry b a e not identical h 

the proportions obtained by computa- 
tion, but they are in the same rat 
which is all that is necessary. They 
may be converted to relative volumes 
by the method described previously. 

Control of Two Constituents 

In considering control of two con- 
stituents, it will be assume that the 
constituents to be controlled are C3S 
and C3A. It should be understoc 
however, that the methods whi will 
be desc bed may be applied to any 
two constituents; for example, to C L >S 
and C3A. Estimation of the propor- 
tions of -lurries to obtain desired per- 

-20 -10 O +'0 

CjS Deviation (P*r cent, unignittd basis) 

Fig. 4: Graphic method for control of one constituent 





+ 20 + 30 + 40 +50 +60 

Potential C*S (Per cent) 
Fig. 5: Graphic method for control of two constituents 



centages of C3S and C 3 A involves 
three successive steps: 

1. The selection of slurries capable 
of forming the desired mixture. 
This is performed graphically. 
Estimation of proportions of the 
lurries. Since CgS and C 3 A are 
expressed on an ignited basis, the 
proportions obtained in this step 
are on an ignited weight basis. 
Since graphic methods are partic- 
ularly advantageous in two-com- 
ponent control, algebraic methods 
will not be discussed. 
Conversion of proportions ob-, 
tained in step 2 to proportions by 
volume, taking into account the 
moisture content of the slurries. 

Step 1. Selection of Slurries. The 
method of sele< ng -lurries may be 
lustrated by referring to Fig. 5. 
In this figure the C*A content is plot- 
ted apainst C3S content. For exam- 
ple, the point designated as K.F. is 
the kiln feed composition, 60% C3S, 
(%A, assumed to be sought in 
Points A, B, C, D and P 
slurries differing in poten- 
and CjA 'content t If a 
straight line connecting any two slur- 
ries passes thi .gh the K.F. point, 
tVe:-e slurries may be combined to 
form the dpsired composition. It will 

m ures. 
tial C S 

be seen then that the K.F. composi- 
tion may be obtained by combining 
slurries A and P, A and D, or C and E. 
Slurries which may be combined in 
pairs to form the K.F. composition 
will be encountered only occasionally. 
Usually three slurries are required. 
In that case the K.F. composition can 
be obtained from three slurries if the 
KJ*. point is inside the triangle 
formed by joining the points repre- 
senting the slurries. For example, 
slurries A, B and C may be combined 
to form the K.F. composition. Cn the 
other hand, slurries £?, C and D can 
not be used, since a triangle joining 
these points would not include the 
K.F. point. 

The graph paper used in the selec- 
tion of slurries should be large, so 
that it can be used in step 2, which 
requires accurate measurements on 
the diagram. The C3S and C3A scales 
should include all values, positive or 
negative, likely to be encountered in 
preliminary slurries. As the composi- 

tThe potential C^S and C .A are calculated 
by substitution in equations 1 and 3. These 
equation? will give negative values o values 
greater than 100 p r cent when the con^titu- 
can not possibly be combined to form the 
compounds C : ,S. C_,S. C a A and C,AF. X 
apparently absi values ar'f plott* d & hou? 
they represented axrtual percentages of the com- 


Ignited basis 

Slurry Slurry Slurry 
A b C 

Unignited (dry) b 

Slurry Slurry 
A B 

as is 



■ Determinations 



18.66 19.80 
5.55 5.95 
3.46 10.57 

70.40 61.87 

72.1 80.4 
35.4 38.4 




Fe O3 





Ignition loss 



CjS , ,. 

........ 15.7 

102.5 46.3 
8.86 —2.11 

calcimeter ). 


Per cent Moisture 
35 3 




*By rapid control metho 
♦♦Calculated by equations 


i acid-alkali or 



tion of each slurry is reported, a point 
representing the slurry is en'ered in 
the diagram, to be erased when the 
slurry is no longer available. The dia- 
gram then also serves as a guide in 
the preparation of preliminary slur- 
ries, since slurry compositions suit- 
able for combination with those al- 
ready available can be seen at a 
glance. The preparation of prelim- 
inary slurries for two-component con- 
trol will be considered in greater de- 
tail after presenting step 2. 

Step 2. Estimation of Proportions 
(Graphic Method). The graphic 
method of estimating proportions of 
materials is an adaptation of a method 
which has long been in use for the 
estimation of phases in the interpreta- 
tion of phase diagrams. The applica- 
tion of this method to the proportion- 
ing of cement raw materials was de- 
scribed in 1927 by E. S., W, S., and 
W. A. Ernst, and in 1929 by R. Grun 
and G. Kunze.* It was first applied 
in routine raw mix ccntrol by R. M. 
Wiilson** and his assistant chemists 
at the Victorville plant of the South- 
western Portland Cement Company. 
In their operations the graphic method 
is used in estimating proportions of 
preliminary slurries, to secure a final 
slurry with desired percentages of 
C a S and C3A. The method is illus- 
trated in Fig. 5. 

The pl:tting of slurry compositions 
(C 3 S and C3A) has been described in 
connection with the selection of slur- 
ries (step 1). The K.F. point can be 
located to represent any desired kiln 
feed composition, but in this figure 
it is assumed that 60% C 3 S, 7% C 3 A, 



the composition sought, Points A, 
and C represent the three slurries 

the above table. 

All of the compositions which can 
be made from two slurries are on the 
straight line joining the slurries. For 
example, slurry F, Fig. 5, can be made 
from slurries B and C. The lengths 
of the lines CP and BP are the rela- 
tive proportions of B and C, respec- 
tively, required to form slurry P. The 
lengths of these lines in the original 
diagram en a larger scale are indi- 
cated in the figure. It is seen that 
20.65 parts by weight of slurry B may 
be combined with 10.8 parts by weight 
of slurry C, to form 20.65 + 10.8, or 
31.45 parts by weight of slurry P.t 
Since the diagram is based upon C3S 
and C :l A percentages on an ignited 
basis, these values are on ignited 
weight basis. 

Following the same procedure, it is 
found that the relative proportions of 
slurries A and P to form the K. F. 
composition are 10.0 and 33.0, respec- 
tively If slurry A is to be used with 
31.45 parts by weight of slurry P (the 
quantity formed from slurries B and 
C), 10 X 31.45/3.0, or 9.53 parts by 

♦Proportioning Raw Materials. Edgar S. 
Ernst, Walter S. Ernst and Wm. A. Ernst. 
Rock Products, Oct. 15. 1927, pp. 73-76. 

A Graphic Method of Proportioning the Raw 
Mix. Dr. Richard Grun and Dr. Gunther Kunze. 
Concrete, Cument Mill Section, Jan., 1920, pp. 

115-12 4. 

♦♦Chief Chemist. Southwestern Portland Ce- 
ment Co., Victorville, Calif. 

t Since the slurry nearer to the desired com- 
position ia used in the greater quantity, the 
length of the line farther from B is the rela- 
tive proportion of B, and the length farther 
from C is the relative proportion of C. This 
principle is followed in every case. 


weight will be required. Thus we have 
the relative proportions of slurries A, 
B and C, as follows: 

Relative proportions 


(ignited weight basis) 







In obtaining the relative propor- 
tions on an ignited weight basis, a line 
was drawn from vertex A through 
the K. F. point to P. Any vertex 
could have been selected fcr the pur- 
pose. For example, a line from vertex 
C through the K. F. point to E might 
be drawn, as indicated by the broken 
line in the figure, and the same pro- 
cedure followed in estimating relative 
proportions of slurries A 9 B, and C. 
The values obtained will not be the 
same as these found above, but they 
will be in the same ratio to one an- 
other, which is all that is necessary. 

Relative proportions on an ignited 
basis are converted to relative propor- 
tions on an unignited basis by divid- 
ing each value by (100 — ignition 
loss)/100, indicated in table below. 

and it is necessary tb check the pro- 
portioning operation by tests for car- 
bonate content. In addition, since this 
method of checking is valid only for 
combinations of two slurries, it will 
be necessary to combine two of the 
three slurries, testing this mixture 
for carbonate content and adjusting 
proportions, if necessary, before add- 
ing the third slurry; that is, the op- 
eration is carried out in two stages, 
each involving the combination of two 

The relative proportions on an un- 
ignited basis are converted to relative 
proportions on a slurry volume basis 
by applying the factors for moisture 

content from Table 3, as shown ai the bottom 
of this page. 


Before proceeding with a descrip- 
tion of the use of carbonate determin- 
ations in obtaining correct propor- 
tions on a dry weight basis, it should 
be emphasized that the carbonate de- 
terminations do not serve the purpose 
when three slurries are combined be- 
fore testing. This is true for two 



Rel. proportions 
(ignited basis) 

100 loss 

Relative proportions 
(unignited basis) 




9.53 -5- 
20.65 4- 
10.8 4- 


= 14.75 
= 33.52 
= 16.82 

In the footnote to Table 3 attention 
is called to the fact that the factors 
for conversion to a volume basis are 
only approximate. In addition, fur- 
ther errors may be introduced because 
of the lack of precision in volume 
measurement of slurry in the plant. 
If the three slurries to be combined 
are all close to the desired mix com- 
position, errors from these causes are 
not likely to be significant, and the 
calculated relative volumes can be 
used without further tests. In this 
case, slurries A, B, and C are not 
close to the desired K. F. composition, 

reasons, as follows. 


Per cent 

(Table 3) 

1. The mixture may be far from the desired 
composition, and yet meet the require- 
ments as to carbonate content. For ex- 
ample all mixtures in the area WXYZ, 
Fig* 5, are within 0.2 per cent of the 
carbonate content of the K. F. composi- 
tion This includes a wid^ range of per- 
centages of C3S and C3A. 

2. If the carbonate content is too far from 
the K. F. composition to be considered sat- 
isfactory, the correction to be applied is 
not known For example, the C3S and 
C3A content of a mixture too high in car- 
bona'es is not known. It may be corrected 
for carbonate content by the addition of 
either slurry A or B (Fig. 5). The fact 
that the carbonate content is high pro- 
vides no information as to which slurry 
will br ; ng it cloier to the K F. composi- 
tion. Th^ wrong choice may even bring it 
farther from the desired composition. 

Relative proportions 
(unignited basis) 









Rel. proportions 
by volume 

VIZ 7 



As will be shown presently, there 
is sometimes a reas:n for choosing a 
particular pair of slurries to be mixed 
first, before adding a third. In the 
case of slurries A, B f and C there is 


Rel. propor- 









X 72.1 = 1063 



X 80.4 = 2695 





- 77Q ^,ov ««» 

-* +- /inrkAnofflo 




Rel. propor- 









76.7 per cent carbonates 

no particular choice. We may select 
any pair, and will select slurries A 
and B arbitrarily. It will be necessary, 
then, to determine the carbonate con- 
tent to be sought when combining 

slurry A and B, and when combining 
this mixture with slurry C. These 
values are found as indicated above. 

It was found previously that slur- 
ries A y B f and C are to be used in 
the proportions 17.3, 46.9 and 22.2 
parts by volume, respectively. The 
procedure is to combine slurries A and 

B in the proportions indicated, then 
determine carb:nate content. If the 
carbonate content departs from 77.9 
per cent to a greater extent than is 
considered satisfactory, an adjust- 
ment in proportions is made. Slurry 
C is then added to the mixture, and 

the carbonate content determined. If 


it departs too much from 76,7 per 
cent, an adjustment should be made. 
Because the mixture of slurries A and 
B already has been adjusted and the 

entire quantity is used in making the. 
final mixture, an excess of slurry C 
should be avoided. In deciding upon 
limits to be assigned to the carbonate 
content, it should be borne in mind 
that a deviation of 0.1 per cent in 
carbonate content is equivalent to 
about 1.4 per cent deviation in C3S. 
By this procedure, with reasonably 
small limits on carbonate content in 
each stage, the potential C3S and C3A 
values sought can be obtained with a 
satisfactory degree of accuracy, even 
though the slurries to be combined 
depart considerably from the desired 

The Preparation of Preliminary 
Slurries. In the procedure which has 
been described, the time consumed in 
obtaining the desired composition in 
each stage depends upon the chances 
of obtaining the calculated carbonate 
content, within assigned limits, when 
proportioning by volume. If the car- 
bonate content is correct in most 
cases, little time is consumed in mak- 
ing adjustments and in testing the 
mixtures after adjustment. On the 
other hand, a great deal of time may 
be consumed in these operations if 
adjustments are usually required. 
On that account, some consideration 
should be given to methods of avoid- 
ing frequent adjustments of propor- 
tions. When such adjustments are re- 
quired too frequently, there is likely 
to be a tendency to widen the limits 
on carbonate content which will be 
accepted as satisfactory. This will re- 
duce the frequency of adjustments, 
but it is not a real solution, since it 
means the acceptance of a wider range 
of percentages of potential C3S and 
C3A in the final mixture. For exam- 
ple, if a carbonate content within 0.7 
per cent of the calculated carbonate 
content is accepted as satisfactory, it 
is equivalent to accepting a range of 
about 14.0 X 0.7, or 10 per cent, on 
each side of the C3S ccntent sought. 
The limits on carbonate content 
should be assigned with reference to 
the range of values of C3S which is 
considered acceptable. If adjustments 
are required too frequently, other 
means of avoiding them should be em- 
ployed. These are concerned with the 
preparation of preliminary slurries 
which are combined to form the final 


Steps which can be taken to simpli- 
fy the operations in control of two 
constituents may be illustrated by ref- 
erence to Fig. 5. As mentioned previ- 
ously, slurries A and B are mixtures 
of limestone and shale, while slurry 
C is a mixture of the same raw mate- 
rials, but with high-iron material 
added to reduce the potential C3A 
content. Let us suppose that the lime- 
stone-shale mixtures are prepared 
more accurately than A and £?, so 
that slurries A\ and R\ are obtained 
instead. Less high-iron material may 
be used in preparing the third slurry, 
obtaining a composition such as C\ 
instead of C. Since slurries A], B\ f 
and C\ are close to the K. F. compo- 
sition, the proportioning operation 
does not need to be carried cut as ac- 
curately as in the case of slurries A t 
B, and C. The three slurries can be 
mixed simultaneously in the calcu- 
lated proportions by volume, and no 
test of carbonate content should be 

The combination of slurries A, B, 
and C and the combination of slurries 
A\, Z?i, and C\ represent two extremes. 
Accurate proportioning of A, B, and 
C requires two stages, each subject to 
check by carbnate determinations, 
with the necessity of frequent adjust- 
ment of proportions. Slurries A\ f B\ t 
and O may be combined in one opera- 
tion, without such tests and adjust- 
ments. The latter condition may not 
be attainable with the equipment 
available in the plant, but an ap- 
proach to it will simplify operations 
in seeking reae nably accurate control 
of two constituents. Anything which 
can be done to bring preliminary mix- 
tures closer to the desired composi- 
tion will reduce the frequency with 
which adjustments of proportions are 
required, even if the need for checking 
by carbonate determinations is not 

There are some instances in which 
the second stage of the proportioning 
operation can be simplified by a prop- 
er choice of slurries to be combined 
in the first stage. For example, let us 
suppose that slurries A, £?, and C\ are 
to be combined to form the K. F. com- 
position. Since C\ and E are close to 
the K. F. composition, slurry E may 
be made by combining A and B t with 

tests for carbonates and adjustment 
of proportions. Slurries C\ and E may 
then be combined in calculated pro- 
portions by volume, without the need 
for carbonate tests. If slurries A and 
Cu or B and Ci, are combined in the 
first stage, conditions are not as fav- 
orable for proportioning by volume, 
and carbonate determinations are re- 
quired in both stages, with the possi- 
bility of a need for adjustment of 
proportions in either stage. 

In the case just described, slurry 
1 is used in greater proportion than 
slurries A and B. At some plants it 
may be convenient to prepare a high- 
iron slurry with such a high percent- 
age of Fei>03 (low or negative C3A) 
that it will be used in small propor- 
tions in each combination. The per- 
centage of Fe203 may be much greater 
than in slurry C, but the procedure 
may be described with reference to 
slurry C. Let us assume that the 
limestone and shale, or equivalent ma- 
terials, are proportioned with a fair 
degree of accuracy, so that slurries 
A\ and B\ are obtained. Slurries A\ 
and B\ may be combined first to form 
slurry E t without carbonate tests, and 
slurry C may then be added, and car- 
bonate tests applied to insure accu- 
racy. On the other hand, if slurries A\ 
and C, or #1 and C, are combined first, 
carbonate tests are required in the 
first stage. In the second stage they 
may be found necessary, but the 
chances are favcrable for obtaining 
the desired carbonate content, with 
few occasions in which adjustment of 
proportions is needed. Here there is a 
choice between simplifying the first 
or second stage. In general, simplifica- 
tion of the second stage is preferable, 
since the total quantity of slurry made 
in the first stage is used in the second 
stage. An adjustment requiring an 
additional quantity of this slurry in- 
troduces an awkward situation which 
can be avoided, at least most of the 
time, by simplifying the second stage. 



Derivation of Equation for Effect 

of an Added Material on the 

Carbonate Requirement 

Equation 7 in the text refers to the effect of 
the addition of iron ore or sand to the raw mix 
on the carbonate requirement. The equation 
has a more general significance, however. It 
refers to the addition of any material, com- 
posed of one or more of the major components 
of Portland cement clinker. For example, the 
equation may be applied to materials used as 
a source of alumina, to a clay or shale not 
originally present in the mix, etc. Because the 
equation does not refer only to the addition of 
iron ore or sand, reference to these particular 
materials will be avoided here, and the added 
material will be referred to as an "additive." 

The symbols used in the derivation arr 

Nhown at the bottom af this page. 

It should be noted that A is the potential 
C3S (or C2S) to be maintained in the mix. 
both before and after the introduction of the 
additive. The quantity p is the carbonate con- 
tent of a correctly proportioned mix before 
the introduction of the additive, that is, p is 
the carbonate requirement. The carbonate con- 
tent is increased by the amount x when the 
additive and limestone are introduced, as- indi- 
cated in the last column. It is the quantity 
x which is sought. The quantity S is 100 minu^ 
the ignition loss in the correctly proportioned 
mix. The value of S need not be known, since 
S drops out in the course of the derivation. 
The sum of the fractional weights of the ma- 
terials is always unity. The fractional weight 
of the original mix is therefore (1— r — s) . 

The percentage of any constituent in the 
final mix is the sum of the products obtained 
by multiplying the percentage of that constit- 
uent in a material by the weight fraction of 
the material. Since carbonates are expressed 
on an unignited basis, the weight fractions on 
an unignited basis are used in setting up the 
equation for carbonates. For a similar reason, 
the weight fractions on an ignited ba^is Are 
used for C3S. The equations obtained in this 
manner are shown below. 

Eliminating & from equations 3 and 4. 

Si I P2— P) iA — A\) 

Pi — P H — 

x = r 

Carbonates : 
P(l — r - 
CrS : 
AS(l —r — s) + AxSir + A*S«8 

3) + P\r + p.* = p + x 

= A 

S + (Si — S)r + (S 2 — S)8 
Collecting terms in equation 1, 

( pi — p) r 4- p>2 — p)s = x 
Upon simplifying equation 2, S drops 
leaving the equation. 

Si (A x — A)r + S2M2 - A)s == 


I I 






S 2 (A 2 — A) 
Let F represent the increase in carbonate re- 
quirement due to the introduction of 1.0 per 
cent of the additive. Then r = 0.01. and 

1 T . Si (p» —p}(A—Ai) 

Pi — P + 

F := 

100 L" 1 " ' So(A« 

which is equation 7 in the text. 



Preparation of Raw Mix Sample 

for Analysis 

The first step in the compiete analysis of a 
raw mix .sample is to render iL acid-soluble by 
fusing it with sodium carbonate or by heating 
it to a temperature high enough to form a 
clinker. Fusion with sodium carbonate intro- 
duces large amounts of sodium salts into the 
solution. As a result, the time required for 
analysis is increased, because double precipita- 
tion is required to secure satisfactory accu- 
racy. On that account it is recommended that 
the sample be prepared for analysis }.. heating 
at a temperature high enough to convert it to 

Burners and muffle furnaces commonly used 
for ignitions and fusions in analytical work do 
not develop the temperatures required for 
clinkering raw mix samples. In some labora- 

mix samples are clinkered in 
forming a button more dense 
linker, to be ground for an- 
temperature furnace of the 
in which the heating elements 
are rods of carborundum, is used in other lab- 

The globar type furnace is convenient in 
some respects, but has the disadvantage that 
it must be kept in continuous operation. Re- 
peated cooling below a dull red heat causes the 
heating elements to deteriorate rapidly. A cru- 
cible furnace utilizing gas and compressed air 
has the advantage that the cold furnace can b< 
brought up to temperature very rapidly, pro- 
ducing a satisfactory clinker in 15 minuses af- 
ter a cold start. The writer has had no expe- 
rience with a gas-fired crucible furnace, but 
our attention has been called to the fact that 
a crucible furnace supplied by the Selas Com- 
pany has proved satisfactory. 

The time and temperature required for ob- 
taining a satisfactory clinker for analysis will 
depend apon the composition of the sample. It 
is advisable to determine the lime or carbonate 
content before clinkering the sample. Sample- 
low in carbonates require a lower temperature, 
<>r less time, than samples high in carbonates. 
Since other components of the mix also have 
an influence, the procedure to be followed mu 
be learned by experience with the materials in 
use at the plant. 

ries the raw 
an electric arc, 
than a normal 
alysis. A high 
"globar" type, 

K^w Mix 




to balance 



mix after 

Weight fractions of materials (unignited weight basis) 

Percentages of constituents 

C 3 S (or CjS) 



100-ignition loss 






Weight fractions of materials (ignited weight basis)* 

*D — S{\ — r — 8) + Sir + S2S - (SiS)r + (S 2 





Bulletin 8 

"Fiexural Vibration of Unrestrained Cylinders 

Disks," by Gerald Pickett, December, 1945. 
Reprinted from J ox al of Applied Physics, 16, 
820 (December, 1945). 




Should Portland Cement Be Dispersed?" by T. C 

Powers, February, 1946. 
Reprinted from Journal of the Amer in Concrete Ii 

stitute (November, 1945) ; Proceed 12, 117 1945). 

Bulled 1 10 

"Interpretation of Phase Diagrams of Ternary Systems," 
by L. A. Dahl, March, 1946. 

Reprinted from The Journal of Physical Ch< y. 50, 

(3) 96 (March, 19 Hi). 

Bulletin 1L — "Shrinkage Str es in Concrete: Part 1 — Shrinkage (or 

Swelling), Its KIT t upon Displacements and Stn in 

Slabs and Beams of Homogeneous, (sotroph Elasth - 
terial; Part 2 — Application of the The j l'i< ented in 
Part 1 to Experimental Results,' by Gl vld PlCKEl 
March, 1946. 

Reprinted from Jon al of th .1 wricai ret( .' 

stitute (Jan. and Feb., L946) ; / 12, 1< 

361 (1946). 

lull HI 1 


Li i H, 

The Influence of t psnm on the Hydr ion and 
ties of Portland Cement Past WILLI i 

March, 1 

Prep at for Proi f ij 

Mat ate. 16 ( 1946). 

Bulletin 1 

-"Tests of Concretes Containing \ir-Ent raining Portland 
Cements or Air-Entraining Materials Add to Batch 

Mixer, ! II. F NNER AN. 

Reprinted from Jour f tl A>> C I 

st e (June, 1 14) ; P> dh 10, 177 (1944) al 

supplementary data at analv rim fr< 

I ut (Noveml L944) ; I 10, 508-1 (1! ) 

Bulletin 1 I 

bulletin 15 

"An Explanation of the Titration Values Obtained in the 
Merriman Sugar-Solubility Tt-i fori rtland ement. ' 


Reprinted from ASTM Bull 1 1 h, 1947) . 

"The Camera Lucida Method for .Measuring Air Voids in 

Hardened Concrete," by <;eorgi Vfrbeck. 
Reprinted from /< f t) u A < I 

(M 1M7> ; Pr 43. 1 

Bulletin 16 

"Development and Study of Apparatus and Me' hod >r 
the Determination of the Air Content of Fresh Concrete, 

by Carl A. Me ^el. 

I print rom J> th< A> C 

tit (May, 194 P 43. 1053 (1947).